As Kaddour

Maturity of 3D failure criteria for fibre-reinforced composites: Comparison between theories and experiments: Part B of WWFE-II

This article draws to a conclusion the results from the co-ordinated study known as the Second World-Wide Failure Exercise (WWFE-II). It contains an objective assessment of the performance of 12 leading failure criteria for predicting the response of fibre-reinforced polymer composites when subjected to 3D states of stress. Twelve challenging test problems (Test Cases) were defined by the organisers of WWFE-II, encompassing a range of materials (polymer, glass/epoxy, carbon/epoxy), lay-ups (unidirectional, angle ply, cross ply and quasi-isotropic laminates) and various 3D stress states (various triaxial strength envelopes, through-thickness and shear loading, and stress–strain curves). A systematic comparison has then been conducted between ‘blind’ predictions (i.e. without access to the experimental results beforehand) made for each Test Case by the originators of each theory and previously obtained experimental results for each Test Case. In-depth quantitative and qualitative ranking procedures have been employed to identify the strengths and weaknesses of each theory, and the overall effectiveness of each theory as a potential design tool. The theories are grouped according to their degree of maturity and ability to predict accurately the 3D behaviour of composites. The results from this study provide unique information to the community, the intent being that it will form a guide for the selection of the most appropriate failure theory for use in a given design situation.

The background to the third world-wide failure exercise

In 2004, the authors completed the First World-Wide Failure Exercise dealing with benchmarking recognised failure criteria under two-dimensional, in-plane loadings. Based on the success and the lessons learnt, and using the same strategy, the authors have organised the ‘Second World-Wide Failure Exercise’. It aims at filling key gaps identified and establishing the status of 12 theoretical methods for predicting failure in fibre-reinforced composite materials subjected to three-dimensional or (triaxial) states of stress. This paper gives an account of the background to the Second World-Wide Failure Exercise, the process of completing the first part (Part A) and a summary of key conclusions.

A comparison between the predictive capability of matrix cracking, damage and failure criteria for fibre reinforced composite laminates: Part A of the third world-wide failure exercise:

This paper provides a set of concluding remarks on Part A of the third world-wide failure exercise where a comparison has been made between the capabilities of 12 different mathematical models for predicting the evolution of matrix cracking, damage and failure in continuous fibre-reinforced polymer composites when subjected to multi-axial loading. The originators (or their collaborators) of those theories have employed their methods to 13 carefully selected challenging problems (test cases) addressing the cracking and damage evolution arising from ply thickness, lay-up sequence, size effects and a variety of loading conditions (biaxial, bending, thermal loading and loading-unloading) of a number of unidirectional and multi-directional glass and carbon epoxy laminates. These covered eight different lay-ups consisting of 0°, [0°/90°/0°], [0°/90°8/0°], [0°/90°]s, [±45°]s, [±50°]s, [30°/90°/−30°/90°]s and a family of [0°m/45°m/90°m/−45°m]s, [45°/0°/90°/−45°]s and [0°/45°/−45°/90°]s quasi-isotropic laminates. Key features in each theory are identified including: types of damage models employed, whether linear or nonlinear analysis was carried out, reliance on software and numerical methods and identification of modes of damage. The results of stress–strain curves, crack density and damage curves have been superimposed and bar charts were constructed to show similarities and differences between the predictions of the various theories.

Input data for test cases used in benchmarking triaxial failure theories of composites

This article gives details of the input data provided for use in the Second World-Wide Failure Exercise (WWFE-II) for benchmarking triaxial failure criteria. It includes (a) three-dimensional elastic constants, ultimate strains and strengths and the nonlinear stress–strain curves for five unidirectional laminae and their constituents and (b) a description of 12 challenging test cases of 5 composite laminates, the lay-ups, layer thicknesses, stacking sequences and the loading conditions. The originators of 3D failure theories were requested to use the exact data provided here in their blind predictions of the test cases. The instructions issued to the contributors are also presented at the end of this article.

Mechanical properties and details of composite laminates for the test cases used in the third world-wide failure exercise

This paper gives details of the input data and a full description of a set of 13 test cases provided to the participants of the third world-wide failure exercise for use in their theoretical models. World-wide failure exercise is aimed at benchmarking leading methods, capable of predicting initiation and progression matrix cracking and damage and failure in composites. The originators of leading theories were requested to use the exact input data provided here in their blind predictions of the test cases. The input data include all of the elastic constants, ultimate strains and strengths and the nonlinear stress–strain curves for the unidirectional laminae and their constituents. Various types of laminates, chosen for the analysis, are described together with the lay-up, layer thicknesses, stacking sequences and the loading conditions. Detailed instructions, issued to the contributors, are also presented at the end of this paper.

Triaxial test results for fibre-reinforced composites: The Second World-Wide Failure Exercise benchmark data

This article describes a unique set of experimental results employed in benchmarking leading three-dimensional failure criteria, as a part of the Second World Wide Failure Exercise (WWFE-II). In Part A of WWFE-II, the originators of those criteria (or their representative) made blind theoretical predictions of the triaxial strength, stress–strain curves and deformation of 12 Test Cases, selected by the organisers to challenge the contributors’ models. The cases covered various materials and laminates subjected to a wide range of triaxial and through-thickness loading conditions. The Test Cases were for (a) an isotropic material made of an epoxy polymer, (b) various 0° unidirectional laminae and (c) (0°/90°)s, (0°/±45°/90°)s and (±35°)s multi-directional laminates. In Part B of WWFE-II, a comparison is made by the contributors between available experimental results, described here, and their theoretical predictions, made in Part A. Discussion is also made on the accuracy of these results.

Benchmarking of triaxial failure criteria for composite laminates: Comparison between models of ‘Part (A)’ of ‘WWFE-II’

As a part of the Second World-Wide Failure Exercise, the originators (or their collaborators) of three-dimensional failure theories applied their methods to 12 carefully selected challenging problems (test cases). In this article, the ‘blind’ theoretical predictions from 12 failure theories, making the backbone of Part (A) of the Second World-Wide Failure Exercise, are compiled in a structured manner. Key features in each theory are identified including: types of failure models employed, whether linear or nonlinear analysis was carried out, reliance on software and numerical methods, allowance for thermal stresses and identification of modes of failure. The results (failure envelopes and stress–strain curves) have been superimposed to show similarities and differences between the predictions of the various theories. In addition, bar charts have been constructed to demonstrate the levels of agreement between the predicted failure stresses and strains. Sources of differences between the predictions of the various three-dimensional failure theories are discussed. Further publications are planned in Part B in which comparison will be made between the predictions described here and the experimental results.

The background to Part B of the Second World-Wide Failure Exercise: Evaluation of theories for predicting failure in polymer composite laminates under three-dimensional states of stress

The Second World-Wide Failure Exercise was launched and organised by the authors to determine the accuracy of current theories for predicting failure in polymer composite laminates under three-dimensional states of stress. This paper provides an introduction to the second stage (‘Part B’) of Second World-Wide Failure Exercise within which the level of maturity and accuracy of the leading three-dimensional failure theories for composites are assessed against experimental data, their strengths and weaknesses are identified and conclusions are drawn. The Second World-Wide Failure Exercise builds upon the process and philosophy developed during the First World-Wide Failure Exercise with the clear aims of ensuring that the assessment is objective, transparent and an effective, accessible benchmark for use by the composites community.

1.23 Failure Criteria for Composites

Failure criteria for composites are the biggest single topic toward which the composites community has been engaged in extensive research initiatives and activities. Perhaps, the most notable activity in the history of composites is that carried out under what is widely known as the world-wide failure exercises (WWFE). Their aim was to independently establish the maturity of existing failure criteria and methodologies, as described and performed by their own originators, and to identify remaining challenges in accurately predicting the strength and deformation of composites. Three exercises were conducted covering more than 30 internationally recognized failure methods and those are (1) WWFE for two-dimensional (2-D) failure criteria, (2) WWFE-II for three-dimensional (3-D) failure criteria, and (3) WWFE-III for matrix cracking damage criteria. The failure criteria/methodologies have been employed by their originators. This chapter aim at piecing together a coherent set of lessons emanating from the three exercises on how the various elements of models/theories can potentially fit together to help the composites design community. Examples are provided in the form of stress–strain curves, failure envelopes, and summary tables on the limitations and the applicability of the various models. Some of the gaps identified are also listed.